This invention relates to a system and apparatus for designing signalling waveforms for Direct-Sequence Code Division Multiple Access Communications (DS-CDMA), and to systems and methods employing or producing such optimal signalling waveforms.
CDMA based wireless communications methods and systems have been introduced and continue to be utilized in digital cellular and PCS (personal communications system) network applications. While much effort at optimizing various aspects of CDMA has been expended, and much of this optimization has been codified in various existing and proposed standards, it is a fact that the current systems use conventional waveform shapes which are not optimized. Waveform shaping is one of the last processes performed in a CDMA transmitter whereby each information element to be transmitted is mapped onto a physical waveform shape.
There has been previous work on the optimization of the chip waveform in DS-CDMA systems. See for example xe2x80x9cPerformance of DS-CDMA Communication Systems With Generalized Offset QPSK Modulationxe2x80x9d by Mohamed Adnen Landolsi, A dissertation submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy (Electrical Engineering: Systems), 1996, The University of Michigan. This work has not taken into account synchronization acquisition and tracking performance. It has been limited in its application to only full-response pulse shapes, not handling the more general case of partial-response pulse shapes.
A system and method are provided for improving DS-CDMA system performance through the careful design of the signalling waveforms.
The improved signalling waveforms provided will optimize a cost function, either by minimizing the multiple-access interference power or by maximizing the acquisition SNR, in either case subject to various constraints on the transmitted signals. The immediate impact of this minimization is an increased system capacity (as measured by the number of simultaneous active users) at a given Grade of Service (GoS) determined by the Bit Error Rate (BER), or equivalently, an improved GoS (i.e., lower BER) achieved for a given fixed number of users.
The invention is pertinent to the electrical signalling formats at the physical layer, and does not involve any upper layer protocol changes. Hence, the optimization proposed is transparent to the network architecture, and will only require some modification at the modem level while keeping consistency with higher layers, which greatly facilitates its incorporation in deployed or soon-to-be deployed systems.
To determine a pulse shape having a Fourier transform for use in a DS-CDMA (direct sequence code division multiple access) communications system, the Fourier transform is first projected onto a truncated set of basis functions fi (xcfx89), thus expressing the Fourier transform as a sum of M+1 terms of the form xifi(xcfx89), where the xi are unknown coefficients, M being an integer selected to result in a sufficiently accurate approximation. Next, a cost function which is either an acquisition SNR or an interference power is expressed as a function of the set of basis functions and the unknown coefficients. The remaining one of the acquisition SNR and interference power is used to express a first constraint in terms of the set of basis functions and the unknown coefficients. The unknown coefficients are numerically solved using mathematical methods software such that the cost function is optimized subject to the first constraint. In some cases, it may be useful to form the Fourier transform by adding up the functions using the solved coefficients. In other cases, the Fourier transform may be used directly to produce filters having the required frequency response.